Stability of Positively Charged Solutes in Water: A Transition from

Jan 7, 2012 - ... to continuum models aimed at predicting the solvation free energies of large ... Tod A. Pascal , William A. Goddard , III , Prabal K...
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Stability of Positively Charged Solutes in Water: A Transition from Hydrophobic to Hydrophilic Tod A Pascal,†,‡ Shiang-Tai Lin,§ William Goddard, III,*,†,‡ and Yousung Jung*,† †

Graduate School of EEWS (WCU), Korea Advanced Institute of Science and Technology, Daejeon, Korea Materials and Simulation Process Center, California Institute of Technology, Pasadena, California 91125, United States § Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan ‡

S Supporting Information *

ABSTRACT: To improve the description of solvation thermodynamics of biomolecules, we report here the dependence of solvation on the curvature and surface charge of positively charged solutes in water based on extensive molecular dynamics simulations analyzed using the two-phase thermodynamic method. At a surface charge of +0.4e, the compensating forces of favorable electrostatic stabilization and entropic destabilization cancel almost exactly, representing a molecular crossover point from hydrophobic to hydrophilic behavior, independent of curvature. These results suggest that one should include charge-dependent entropic corrections to continuum models aimed at predicting the solvation free energies of large biomolecules.

SECTION: Statistical Mechanics, Thermodynamics, Medium Effects

T

iodide using an ultrashort laser pulse,18 demonstrating that large ions may display hydrophobic behavior in solution. These studies and others all indicate a charge-dependent, molecular crossover point from hydrophobic to hydrophilic character, although this has not been clearly demonstrated. Here, we quantify the entropic penalty of ordered water structure due to electrostatic attractions between charged species and water at the interface, which affects the interfacial properties of water so important for such basic phenomena as dissolution. Thus, we address these issues by explicitly calculating the entropy (TΔS0) and free energy (ΔA0) of water in the presence of a variable sized solute of charge states ranging from 0 to +1e. Our results are based on extensive molecular dynamics simulations using the LAMMPS19 simulation engine in the isobaric (1 atm), isothermal (298 K), or NPT ensemble. Spherical cavities with hard-sphere radii of 0 ≤ rHC ≤ 15 Å were created inside of pre-equilibrated cubic water boxes (216−3305 water molecules) described using the extended simple point charge (SPC/E) water potential.20 The SPC/E water model has been extensively used in solvation studies4,11,13,21 and is used here for convenience and computational efficiency. We note that while the solvation thermodynamics is somewhat sensitive to the choice of water model,11,21−23 the solvation trends should be less so, if only due to cancellation of errors.

he solute−water interactions that determine the solubility of biomolecules such as proteins and DNA in water depend on size, geometry, and surface character. Due to this complexity, simplified models have been employed to obtain a qualitative understanding of the forces that determine stability. For example, from calculations of the change in the free energy of water due to the presence of spherical, nonpolar solutes of increasing size, several studies1−3 have proposed the existence of an entropic driving force for assembly of large proteins in water.5,6 The solutes in these studies are hydrophobic, in sharp contrast to solvation of real ions, which are strongly hydrophilic and characterized by large solvation free energies. The extreme case is that of the proton (H+), where both experiments7,8 and theory9 estimate a solvation energy of −1050 kJ/mol. Theoretical studies on the solvation of ions in water revealed a quadratic dependence on charge,10 although the polarizability of the ions as well as the asymmetry of the water molecule and the tendency for water to hydrogen bond to anions lead to a measurable difference in the solvation thermodynamics of similarly sized cations and anions.11,12 Other studies have shown that nanoscale solutes can be hydrophobic while having a surface charge distribution.13−15 Experimentally, a femtosecond mid-infrared spectroscopy study suggested that hydrophobic groups are surrounded by effectively immobilized water molecules in the first solvation shell,16 a claim that has been disputed.17 More recently, picosecond and femtosecond X-ray absorption spectroscopy was used to probe the changes of the solvent shell structure upon electron abstraction of aqueous © 2012 American Chemical Society

Received: December 7, 2011 Accepted: January 6, 2012 Published: January 7, 2012 294

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Ewald tolerance parameter of 10e−4. Absolute entropies and quantum corrections to the internal energy were calculated from additional 20 ps MD trajectories using the two-phase thermodynamic (2PT) method25 every 100 ps. Convergence in the thermodynamics was obtained after 0.5 ns. In the 2PT method, the density of states of the system was obtained from a Fourier transform of the integrated velocity autocorrelation function. The diffusive component of the power spectrum was extracted, and the thermodynamics were determined from hard-sphere theory, while the thermodynamics of the remaining component were determined from Debye theory of a vibrating crystal. The 2PT method has been validated to reproduce the free energy of liquid water along the water−vapor coexistence curve26 and for bulk water from classical26 and ab initio MD trajectories,27 and recently, it was used to determine the thermodynamics of water confined in carbon nanotubes,28 hydrogels,29 and the stability of hydrocarbons.30 We exploit the efficiency of the 2PT method when calculating the system thermodynamics at 100 ps intervals over the final 5 ns of dynamics. The reported statistics are the average of 50 data points, representing a mere 10% increase in computational time, while the quoted deviations are the measured variance. Of course, the various approximations made in our model will have to be validated on proven systems. We do this by calculating the solvation free energy of monovalent cations (RHC = 0 in all cases, i.e., an imaginary point charge without size) by combining recently reported LJ12−6 parameters,21 our solute model, and the Yukawa potential (without any adjustments). As detailed in Table S2 (Supporting Information), the solvation free energies of Li+ (ΔG0 = −442.22), Na+ (ΔG0 = −399.60), and K+ (ΔG0 = −306.18) show a 98% correlation with experiments8,31 and overall good agreement with previous computational results.32,33 Coulombic potentials are long-ranged; therefore, our results using short-range potentials may appear surprising. Previous simulations results have indeed shown that using similar interaction potentials accurately captures the solvation thermodynamics of real ions in water.34 Thus, we reason that the Coulombic field produces highly localized perturbation of the water structure around the ion that does not disrupt the longer-range hydrogen-bonding network. This is consistent with femtosecond pump−probe35 and vibrational O−H spectroscopic36 studies, which demonstrated that the respective rotational and vibrational dynamics of water around small ions converge to the bulk beyond the first solvation shell. Figure 2 shows the energies of solute solvation, referenced to a bulk water box. As expected, the hydrophilicity of the solute increases with increasing surface charge; for He0, it ranges from +22.6 kJ/mol at RHC = 0 to +1565.9 kJ/mol at RHC = 15 Å, while for He+, it ranges from −139.5 kJ/mol for RHC = 0 to −3239.8 kJ/mol at RHC = 15 Å. In other words, the surface tension γ∞ (i.e., the change in free energy per unit surface area)

We initiate the simulations by removing any water molecules in the interior and within 2 Å of the virtual solute surface while ensuring a 10 Å water buffer in each direction (Table S1 of Supporting Information). The oxygen atoms interact with the closest contact point on the surface of the solute (Figure 1)

Figure 1. Interaction potentials of the oxygen on water with repulsive Erep = 1.368[(3.03/Δr)12] (green), attractive ELJ12−6 = 1.368[(3.03/ Δr)12 − (3.03/Δr)6] (yellow) solutes used in this study. The hydrogen (blue, qi = +0.4238) and oxygen (red, qi = −0.8476) of the water molecules also interact with the solutes electrostatically through Yukawa potentials EYukawa = 98.7(qiqj/Δr)e−0.33Δr where qj is the surface charge of the solute. The Yukawa potentials are scaled by a factor of 10 for presentation purposes. All potentials are tapered smoothly to zero from 7−8 Å using a 7th order taper function (not shown).

through a Lennard-Jones 12−6 (LJ12−6) potential, assuming the parameters of helium24 and geometric combination rules with the SPC/E parameters, εij = (εiεj)1/2 and σij = (σiσj)1/2, which result in ε = 0.342 kJ/mol and σ = 3.03 Å. By requiring that the water molecule interact with the solute surface, we guarantee that the water molecules feel a uniform field, irrespective of solute curvature, thus allowing unambiguous probing of the curvature effect. We approximate the electrostatic interactions using a Yukawa (screened coulomb) potential

Eelec = A

qiqj

e−κr

(1) r − where qi is the charge of oxygen (−0.8476 e ) or hydrogen (+0.4238 e−), qj is the surface charge of the solute, A = 98.7 kJ/ mol is an energy conversion parameter, and the Debye screening length 1/κ = 3 Å represents a 1.0 M ion concentration. Because we are simulating an infinitely periodic system, the unit cell necessarily needs to be neutral. Thus, our choice of a Yukawa potential circumvents the need to place a compensating charge in the unit cell or application of neutralizing background corrections to the energies. While this choice may appear limiting, we show later that our description of the electrostatics give results in good agreement with explicit charge calculations. We further require that the energy and forces of our interaction potentials converge smoothly to zero at 8 Å by means of a seventh-order taper function. We performed 5 ns of NPT equilibration dynamics followed by an additional 5 ns of production dynamics for each system. The temperature coupling constant was 0.1 ps, while the pressure piston constant was 2.0 ps. The long-range electrostatics interactions were evaluated by the PPPM method, with a

γ∞ =

ΔA0 4πR2

(2)

at the macroscopic limit decreases with increasing surface charge. It is +61.3 dyn/cm for neutral solutes with LJ12−6 surface potentials to +50.5 dyn/cm for 0.3 e and −130.1 dyn/ cm for 1.0 e solutes. As a figure of merit, the calculated surface tension, extrapolated to the macroscopic limit, of a neutral repulsive solute (meant to mimic the air−water interface) is 295

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other words, the short-range forces conspire to determine the solvation free energy of real ions in water in ways that cannot be captured by ionic radii alone as in our model solutes. Interestingly, we find that a surface charge of 0.4 e corresponds to the molecular crossover point from hydrophobic to hydrophilic behavior. The thermodynamic cost of solute creation is near zero for small solutes (−26.6 ± 10.9 kJ/ mol at RHC = 0), intermediate (−44.9 ± 15.7 kJ/mol at RHC = 6 Å) for intermediate-sized solutes, and large (25.0 ± 30.2 kJ/ mol at RHC = 15 Å) for large solutes. Indeed, for q = +0.4 e, the calculated solvation free energy is found to be close to zero over the entire range of solute sizes (Figure 2), indicating that at this surface charge, the surface tension is nearly zero and water molecules view the solute as if it were another water molecule. It is interesting to note that the hydrophobic/hydrophilic crossover point of q = +0.4 e is practically equal to the charge of the water H atom in the SPC/E model (+0.417 e), thus underscoring the delicate balance between dispersive and electrostatic forces in liquid water. Further insights into the nature of the thermodynamics at various charge states can be obtained by separately considering the enthalpic and entropic components of the free energy (see Figure 4)

Figure 2. Free-energy cost solvation from explicit MD simulations and the 2PT method for creation of solutes of various sizes RHC for various surface charge states from 0 to +1 e. The hydrophilicity of the solute increases with increasing surface charge, crossing over from hydrophobic to hydrophilic behavior at +0.4 e. A purely repulsive solute (red) is referenced.

67.0 dyn/cm, which is in reasonable agreement with the range of 73.6−71.8 dyn/cm from previous studies using the SPC/E water model37 and with 72 dyn/cm from experiment (Figure 3).

Figure 4. Components of the free energy (green squares) of the +0.4 e solute as a function of solute radius. The total entropy (−TΔS, blue circles) and enthalpy (red triangles) cancel almost exactly for all solute sizes, resulting in a net zero solvation free energy. The data points are smooth with a Bezier function (lines) for presentation purposes, and uncertainties are indicated by vertical bars.

Figure 3. Change in the surface tension (ΔA0/dA) of the SPC/E water box with solutes of total radius R (R = RHC + Rs, where Rs = 1.8 Å is the radii of a water molecule). The solid lines are best-fit Bezier functions of the data points. γexp is the experimental surface tension of water, γrep is the surface tension using a purely repulsive surface potential (red), γLJ12−6 is the apolar LJ12−6 surface potential (blue), and γ0.1e (green), γ0.3e (brown), and γ0.4e (cyan) are for LJ12−6 surface potentials with 0.1, 0.3, and 0.4e excess Coulombic charges, respectively.

ΔA0 = ΔE 0 − T ΔS 0

(3)

where the free water box26 is taken as the reference. For typical nonpolar solutes,4 the solvation entropy is unfavorable for RHC ≤ 6 Å and then crosses over, becoming favorable for larger solutes (see the inset of Figure 5). This crossover is related to a transition from a molecular-sized surface to a bulk interface where dangling OH bonds appearing at the interface lead to enhanced rotational and translational entropy and hence increased entropy. In contrast, solutes with +0.4 e surface charge have unfavorable entropy and are destabilized for all sizes without such a transition. In fact, all positively charged solutes have unfavorable entropy for all sizes (Figure 5) due to the increased ordering of the water structure near the surface. On the other hand, the additional electrostatic interactions stabilize the solutes, overcoming both the entropic loss due to a stronger and more rigid binding of water molecules and the energy loss due to broken hydrogen bonds at the interface for

The solvation free energy of solutes with +1 e surface charge decreases monotonically with radii. This result is in contrast with the relationship between solvation free energies and ionic radii of the alkali ions, Li+ (0.9 Å) < Na+ (1.16 Å) < K+ (1.52 Å) < Rb+ (1.66 Å). This apparent discrepancy arises from the difference in the ion-dependent versus size-independent shortrange London dispersive force and Pauli repulsion. The Pauli repulsion is a measure of the “hardness” or atomic polarizability and varies with radii; a measure of this variance can be obtained by comparing the ε and σ parameters in Table S1 (Supporting Information). Our approach, on the other hand, of using the same He parameters for all solutes was chosen to isolate the curvature and charge effects on the solvation, which allows a more systematic investigation of solvation thermodynamics. In 296

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ASSOCIATED CONTENT

S Supporting Information *

Tables of simulation setup and energies. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (W.G.); [email protected] (Y.J.).

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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (WCU R31-2008-000-10055-0, 2010-0029034) with partial support by grant NSC 100-2221-E-002-175 from the National Science Council of Taiwan. The authors acknowledge the generous allocation of supercomputing time from the KISTI supercomputing center at KAIST.

Figure 5. Relative entropy per unit surface area of charged solutes, relative to the nonpolar LJ12−6 solutes (Δ[TΔS]/dA. The color scheme is the same as that in Figure 1. (Inset) Comparison of repulsive (red circles) and LJ12−6 (blue squares) solutes. The crossover radius, Rcross, where the entropy crosses zero at 298 K is calculated to be 6.0 Å for the repulsive solute, in general agreement with results from scaled particle theory.4 The additional dispersive interactions of the LJ12−6 solutes shifts Rcross to 9.8 Å.

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REFERENCES

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